<h2>题目编号 : 188</h2>
<div style="color:#666;font-size:80%;">04 April 2008</div><br />
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<p>The <span style="font-style: italic">hyperexponentiation</span> or <span style="font-style: italic">tetration</span> of a number a by a positive integer b, denoted by a&uarr;&uarr;b or <img src="" style="display:none;" alt="^(" /><sup>b</sup><img src="" style="display:none;" alt=")" />a, is recursively defined by:<br /><br />
a&uarr;&uarr;1 = a,<br />
a&uarr;&uarr;(k+1) = a<img src="" style="display:none;" alt="^(" /><sup>(a&uarr;&uarr;k)</sup><img src="" style="display:none;" alt=")" />.</p>
<p>
Thus we have e.g. 3&uarr;&uarr;2 = 3<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> = 27, hence 3&uarr;&uarr;3 = 3<img src="" style="display:none;" alt="^(" /><sup>27</sup><img src="" style="display:none;" alt=")" /> = 7625597484987 and 3&uarr;&uarr;4 is roughly 10<img src="" style="display:none;" alt="^(" /><sup>3.6383346400240996*10^12</sup><img src="" style="display:none;" alt=")" />.</p>
<p>Find the last 8 digits of 1777&uarr;&uarr;1855.</p>
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